Help on Proofs (Rules of Inference)

I'm having a lot of trouble with proofs and rules of inference, If somebody could talk me through each of these problems I will be grateful. Proofs are very interesting to me and I know I need practice, but help is always appreciated.

I'm having a lot of trouble with proofs and rules of inference, If somebody could talk me through each of these problems I will be grateful. Proofs are very interesting to me and I know I need practice, but help is always appreciated.

* = conjunction

(P > T) * P
(T v S) > (T > R)
------------------
(T*P) * R

Let's see if I can write this the "usual" way AND "translate" it. You do the formal writing:

-- for this to be true both sides must be true, so P is true but then also T has to be true for to be true.

-- The left side here is always true since T is, so the right side must be true as well, and since T is true also R is true--------------------------------------- -- follows at once frome the above

R > (Q > S)
P * R
T > P
T v Q
-----------------
SvP

Hint: the second line tells us that both P, R are true...and this is pretty much you need!Now you try the other ones by yourself.

TonioPs. Of course, you must thoroughly know the truth tables for the different connectives...!